Determine the end behavior for function ƒ(x) = –x4 + 5x3 – 3.

f(x)→−∞ as x→−∞ and f(x)→−∞ as x→∞

Step-by-step explanation:

Since the leading term of the polynomial (the term in a polynomial which contains the highest power of the variable) is −x4, then the degree is 4, i.e. even, and the leading coefficient is −1, i.e. negative.

This means that f(x)→−∞ as x→−∞ and f(x)→−∞ as x→∞.